Phase Transitions of Simple Systems

by Smirnov, Boris M.; Berry, R. Stephen

ISBN13: 9783540715139

ISBN10: 3540715134

Format: Hardcover

Pub. Date: 2007-10-01

Publisher(s): Springer Verlag

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Summary

This monograph develops a unified microscopic basis for phases and phase changes of bulk matter and small systems in terms of classical physics. The origins of such phase changes are derived from simple but physically relevant models of how transitions between rigid crystalline, glassy and fluid states occur, how phase equilibria arise, and how bulk properties evolve from those of small systems.

Author Biography

R. Stephen Berry is James Franck Distinguished Service Professor Emeritus in the Chemistry Department at The University of Chicago. He has studied phase changes and phase equilibria for twenty years. He is a MacArthur Fellow and a Member of the National Academy of Sciences of the U.S.A., and has been author or coauthor of five books prior to this. He and his coauthor of this book have known each other for over 40 years, from the time both were working on atomic collision processes. They have been collaborating for about 10 years, in their studies of clusters and of phase transitions.Boris M. Smirnov is a distinguished physicist who worked for many years at the Institute for Ball Lightning, prior to his joining the Institute for High Temperatures in Moscow.

Introduction	p. 1
Thermodynamics of Ensembles of Classical Particles
Excitations in Simple Atomic Ensembles	p. 7
Thermodynamics and Dynamics of Particle Ensembles	p. 7
Interaction of Inert Gas Atoms	p. 9
Similarity Law for Simple Atomic Ensembles	p. 13
Evolution of Particle Ensembles	p. 13
Voids as Elementary Configurational Excitations	p. 17
Structures of Ensembles of Interacting Particles	p. 21
Close-Packed Structures	p. 21
Shells in Close-Packed Structures	p. 24
Lennard-Jones Crystal	p. 27
Morse Crystal	p. 29
Surface Energy of Lennard-Jones and Morse Crystals	p. 30
Solid and Liquid Inert Gases Near the Triple Point	p. 33
Thermodynamics of Dense Gases and Liquids	p. 39
Equation of State for an Ensemble of Randomly Distributed Particles	p. 39
Equilibrium of Gas and Condensed States	p. 42
Liquid Surface Parameters	p. 45
Peculiarities of Similarity for Inert Gases	p. 47
Scaling Law for Molecular Systems	p. 48
Clusters with Short-Range Interaction	p. 51
Configurations of Solid Clusters with Pairwise Atomic Interactions	p. 51
Peculiarities of Close-Packed Clusters with Short-Range Interaction	p. 53
Constructing fcc-Clusters with Short-Range Interaction	p. 54
Growth of fcc Clusters with Short-Range Atomic Interaction	p. 56
Regular Clusters of Close-Packed Structures	p. 59
Icosahedral Clusters	p. 64
Competition of Icosahedral and Close-Packed Structures	p. 67
Ensembles of Classical Particles with Repulsion	p. 75
Thermodynamics of Ensembles of Repelling Particles	p. 75
A System of Hard Spheres	p. 77
Colloid Suspensions as Systems of Repelling Particles	p. 80
Virial Theorem and Instability of Crystal Structure	p. 82
Phase Transition for an Ensemble of Repelling Atoms	p. 88
Phase Transitions in Inert Gases under High Pressure	p. 90
Structures of an Ensemble of Repelling Particles at Low Temperatures	p. 94
Configurational Excitations and Aggregate States of Ensembles of Classical Particles
Configurational Excitation and Voids in Ensembles of Bound Classical Atoms	p. 99
Separation of Thermal and Configurational Degrees of Freedom of Clusters	p. 99
Lattice Model for the Order-Disorder Phase Transition	p. 100
Chemical Equilibria and Phase Transitions	p. 102
Internal Voids in a System of Identical Particles	p. 105
Void Formation in Two Dimensions	p. 109
The Cell Model for Disk Particles	p. 113
Peculiarities of Configurational Excitation for Bulk Atomic Systems	p. 115
Two-State Approximation for Aggregate States	p. 117
Configurational Cluster Excitation with Pairwise Interactions	p. 121
Peculiarities of Configurational Excitation of Clusters	p. 121
Structural Phase Transition in a Solid Cluster	p. 127
Configurational Excitation of the Icosahedral Cluster of 13 Atoms	p. 131
The Cluster as a Microcanonical Ensemble of Bound Atoms	p. 134
The Cluster as a Canonical Ensemble of Bound Atoms	p. 137
Configurational Excitation of the Icosahedral Cluster of 55 Atoms	p. 140
Character of Configuration Transitions in Clusters	p. 146
Phase Transitions in Macroscopic Systems of Atoms	p. 149
Configurational Excitation of a Solid	p. 149
Modified Lattice Model for Configurational Excitation	p. 151
Parameters of Voids for Liquid Inert Gases	p. 153
Voids in a Macroscopic System of Bound Atoms	p. 157
Criterion of Existence of the Liquid State	p. 157
Freezing Points for Bulk Inert Gases	p. 160
General Liquid Properties	p. 161
Melting of Clusters and Bulk Atomic Ensembles	p. 163
Entanglement of Thermal and Configurational Excitations in Clusters	p. 163
Parameters of Melting	p. 165
Contradiction Between the Melting Criterion and Its Nature	p. 170
Definition of the Cluster Aggregate State	p. 171
Voids as Gateways to Fluidity	p. 173
Liquid-Gas Interface	p. 175
Dynamics of Configurational Excitations in Ensembles of Classical Particles
Coexistence of Cluster Phases	p. 179
Hierarchy of Equilibrium Times in Clusters	p. 179
Character of Phase Coexistence in Clusters: Surface Melting	p. 181
Two-Temperature Regime for Cluster Equilibrium	p. 185
Entropy of an Isolated Cluster in the Two-State Approach	p. 187
Temperatures of an Isolated Cluster Near the Melting Point	p. 189
Cluster Heat Capacity Near the Phase Transition	p. 192
Glassy States of an Ensemble of Bound Atoms	p. 199
Glassy State fromthe Void Standpoint	p. 199
Diffusion of Voids in a Bulk Ensemble of Atoms	p. 200
Cell Model for Vacancy Diffusion Coefficients	p. 202
Kinetics of Transitions Between Aggregate States	p. 204
Formation ofa Glassy State	p. 206
Saturated Vapor Pressure Over a Surface in a Glassy State	p. 207
Glassy State for an Ensemble of Repelling Particles	p. 211
More Peculiarities of Glassy States for Simple Atomic Systems	p. 213
Transport of Voids in Nucleation Processes	p. 217
Peculiarities ofNucleation Processes	p. 217
Transport of Voids in a Nonuniform Bulk Atomic System	p. 219
Growth of a Solid Cluster Inside a Liquid as Transport of Voids	p. 222
Wave Mechanism of the Phase Transition	p. 225
Conclusion and Summary	p. 231
References	p. 233
Index	p. 243
Table of Contents provided by Publisher. All Rights Reserved.